A closed form beam element for failure analysis in frame structural systems is developed, which is based on Timoshenko beam theory and the strong discontinuity approach. Nonlinear material behavior is modeled by multiple rotation and transverse discontinuities, which are represented as plastic hinges and dislocations, respectively. The mathematical and physical principles are formulated based on a Lagrangian variational model. The boundary value problem and expressions for beams [1] are derived by solving the proposed formulation using conventional methods of calculus of variations. A thick beam element with multiple strong transverse and rotation discontinuities is derived based on these closed form solutions, which has the capability to model the occurrence of damage. By coupling this beam element with the bar element with a discontinuity [2], which is also formulated from expressions [3], a thick beam-column element with multiple discontinuities is obtained. The closed form symmetric flexibility matrix of the thick beam element with multiple transverse and rotation discontinuities is obtained by evaluating the closed form expressions for a basic system without rigid-body displacement modes. From this matrix, a closed form symmetric stiffness matrix of the thick beam element is naturally developed. In these matrices, there are no additional degrees of freedom associated with multiple discontinuities, they are not derived from the finite element method, they do not use any Gauss integration scheme, their coefficients are not defined in terms of integrals and any type of loads are modeled. It is observed that the formulated thick beam element is mesh independent because the global response of structures is obtained by meshing with a single element per structural member. Considering multiple discontinuities leads to results similar to those obtained with finite elements with distributed plasticity. In addition, the complex snap-back behavior in structures is adequately modeled.